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Table 1 Chi-square fitting procedure using the GPD approach.

From: Distribution of maximum earthquake magnitudes in future time intervals: application to the seismicity of Japan (1923–2007)

h

6.05

6.15

6.25

6.35

6.45

r

7

7

6

6

6

degrees of freedom

5

5

4

4

4

ξ

−0.0468

−0.2052

−0.2137

−0.2264

−0.1616

s

0.5503

0.6420

0.6397

0.6264

0.6081

M max

17.87

9.43

9.31

9.11

10.20

Q0.90 (10)

8.73

8.32

8.29

8.24

8.52

P exc

0.0753

0.2791

0.3447

0.3378

0.1747

  1. The parameters are estimated by minimizing S(ξ, s), defined by expression (21). Mmax is the rightmost point of the magnitude distribution given by expression (3). Q0.90(10) is the 90% quantile of the maximum magnitude distribution (T-maximum magnitude) in 10-year intervals.